Uniformly quasiregular mappings on elliptic riemannian manifolds

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.advisorMathematicsen
dc.contributor.authorKangaslampi, Riikka
dc.contributor.departmentMatematiikan ja systeemianalyysin laitosfi
dc.date.accessioned2012-08-20T07:36:25Z
dc.date.available2012-08-20T07:36:25Z
dc.date.issued2008
dc.description.abstractIn this thesis we study uniformly quasiregular (abbreviated uqr) mappings on compact riemannian manifolds. We prove that the Julia set Jf of a uqr-mapping f : Mn → Mn on a compact riemannian manifold Mn is non-empty. We extend the rescaling principle from euclidean spaces to families of quasiregular mappings between a euclidean space and a riemannian manifold. Thus we can use the rescaling principle to obtain from the family (f j) of the iterates of the uqr-mapping f on the manifold M a quasiregular mapping g : ℝn → Mn defined in the whole space ℝn. Combining these results, we notice that if there exists a uqr-mapping on a compact riemannian manifold Mn, there exists a quasiregular mapping g : ℝn → Mn. In other words, the manifold Mn is quasiregularly elliptic. The converse result is proved in three dimensions: we construct a uqr-mapping on each oriented quasiregularly elliptic 3-dimensional compact riemannian manifold.en
dc.format.extentVerkkokirja (948 KB, 69 s.)
dc.format.mimetypeapplication/pdf
dc.identifier.isbn978-951-22-9425-1
dc.identifier.isbn951-41-0989-9 (printed)#8195;
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/4497
dc.identifier.urnURN:ISBN:978-951-22-9425-1
dc.language.isoenen
dc.publisherTeknillinen korkeakouluen
dc.subject.keyworduniformly quasiregular mappingsen
dc.subject.keywordriemannian manifoldsen
dc.subject.keywordelliptic manifoldsen
dc.subject.keywordZalcman's lemmaen
dc.subject.keywordJulia seten
dc.subject.keywordLattès mappingsen
dc.subject.otherMathematicsen
dc.titleUniformly quasiregular mappings on elliptic riemannian manifoldsen
dc.typeG4 Monografiaväitöskirjafi
dc.type.dcmitypetexten
dc.type.ontasotVäitöskirja (monografia)fi
dc.type.ontasotDoctoral dissertation (monograph)en
local.aalto.digiauthask
local.aalto.digifolderAalto_67220
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